Proof of the Umbral Moonshine Conjecture
Abstract
The Umbral Moonshine Conjectures assert that there are infinitedimensional graded modules, for prescribed finite groups, whose McKayThompson series are certain distinguished mock modular forms. Gannon has proved this for the special case involving the largest sporadic simple Mathieu group. Here we establish the existence of the umbral moonshine modules in the remaining 22 cases.
 Publication:

arXiv eprints
 Pub Date:
 March 2015
 arXiv:
 arXiv:1503.01472
 Bibcode:
 2015arXiv150301472D
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Number Theory;
 11F22;
 11F37
 EPrint:
 56 pages, to appear in Research in the Mathematical Sciences